An inertial proximal splitting method with applications

ABSTRACT

In this paper, we propose an inertial proximal splitting method for solving the non-convex optimization problem, and the new method employs the idea of inertial proximal point to improve the computational efficiency. Based on the assumptions that the sequence generated by the new method is bounded and the auxiliary function satisfies the Kurdyka–Łojasiewicz property, the global convergence analysis with a more relaxed parameter range is proved for the proposed method. Moreover, some numerical results on SCAD, image processing and robust PCA non-convex problems are tested to demonstrate the effectiveness and superiority of the proposed method.

KEYWORDS:

• Multi-block non-convex optimization
• splitting method
• inertial proximal point method
• Kurdyka–Łojasiewicz property
• global convergence

Acknowledgments

The authors wish to thank the Editor-in-Chief Prof. Christiane Tammer and the anonymous referees for providing their valuable suggestions, which have significantly improved the quality of our paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [grant number 72071202], the Postgraduate Research & Innovation Program of Jiangsu Province (Research on Theory and Applications of First-Order Non-convex Optimization Algorithm, KYCX22_2491) and the Graduate Innovation Program of China University of Mining and Technology (Research on Theory and Applications of First-Order Non-convex Optimization Algorithm, 2022WLKXJ021).